A quick check shows that my Supporter blog has the Dashboard -> Settings -> Google Analytics page while my non Supporter blog does not so I'm going to say yes, you have to be a supporter for the Analytics code to be in there.
There was also a problem a long while back (Maybe last year) where you had to input the code again to get it to work. That's when Google switched over the javascript codes I believe.
edit: Found it: http://theedublogger.com/2009/02/21/have-you-re-inserted-your-google-analytics-tracking-code/
Considering it's javascript and you can input javascript here, you may want to try inserting the script into the end of a text widget and see if you can get away with that.
Hope this helps,
-drmike
Problem: no data in my Google Analytics reports.
Blog: historicity.edublogs.org
Background: My edublog has Google Analytics embedded in it. Last year it was tracking quite happily and I was receiving information about traffic to the blog. This year I am getting nothing at all.
Any checks that have been run on the code say that it is fine. Google Analytics confirm that it is tracking correctly as does sitescanga.com. I am at a loss as to why I would not be receiving any data on traffic to my edublog when I know that students have been visiting it.
Do I have to be an edublogs supporter to have Google Analytics working correctly?
Cheers, Tim